Sequential Correct Screening and Post-Screening Inference

TL;DR

This paper introduces Sequential Correct Screening (SCS) for reliably identifying top variables and a post-screening inference method to construct confidence intervals with FCR control, supported by theoretical guarantees and empirical validation.

Contribution

It proposes a novel sequential screening method with anytime validity and a FCR-controlled inference procedure, advancing variable selection and inference in high-dimensional settings.

Findings

SCS provides high-probability guarantees for top-m variable inclusion.

The PSI procedure controls false coverage rate in post-screening inference.

Simulation and real data demonstrate the effectiveness of the methods.

Abstract

Selecting the top-$m$ variables with the $m$ largest population parameters from a larger set of candidates is a fundamental problem in statistics. In this paper, we propose a novel methodology called Sequential Correct Screening (SCS), which sequentially screens out variables that are not among the top-$m$. A key feature of our method is its anytime validity; it provides a sequence of variable subsets that, with high probability, always contain the true top-$m$ variables. Furthermore, we develop a post-screening inference (PSI) procedure to construct confidence intervals for the selected parameters. Importantly, this procedure is designed to control the false coverage rate (FCR) whenever it is conducted -- an aspect that has been largely overlooked in the existing literature. We establish theoretical guarantees for both SCS and PSI, and demonstrate their performance through simulation studies and an application to a real-world dataset on suicide rates.